Stir together cumin, coriander, pepper, cinnamon, and salt in a shallow bowl. Pat tenderloins dry and dredge in spice mixture until evenly coated.

Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking. Reduce heat to moderate and cook pork, turning occasionally, until meat is browned on all sides and thermometer inserted diagonally into center of each tenderloin registers 145°, 20 to 25 minutes. Transfer pork with tongs to a cutting board (reserve skillet) and let stand 10 minutes.

While pork stands, pour off and discard any fat from skillet, then add pomegranate juice to skillet and boil over moderately high heat until reduced to about ⅔ cup about 3 minutes (if side of skillet begins to scorch, reduce heat to moderate). Stir together cornstarch and water and whisk into juice, then boil sauce until thickened slightly, 1 to 2 minutes.

Remove from heat and add vinegar to taste, then swirl in butter until incorporated. Pour sauce through a fine-mesh sieve into a bowl and skim off any fat. Season with salt. Slice pork and serve with sauce.